Hi Tigerlily11
You are correct, it is not called Support Group payment, when you apply for UC it is called LCWRA, one of you can also claim the care element, the one who claims the care element cannot claim LCWRA, so who ever claims the LCWRA then their partner needs to claim the care element.
You should initially be no worse off as you should be entitled to Transitional Protection.
Gary
Nothing on this board constitutes legal advice - always consult a professional about specific problems